1. Field of the Invention
The present invention relates to a pattern determination method and an aperture employed in an exposure apparatus. More particularly, the present invention relates to a pattern determination method for facilitating determination of whether an optical image of an interconnection pattern is formed or not in setting the width of an interconnection and distance between adjacent interconnections in the interconnection pattern of a semiconductor device, and an aperture employed in an exposure apparatus that has light proximity effect reduced in the interconnection pattern.
2. Description of the Background Art
The semiconductor industry is moving rapidly towards microminiaturization in the pattern of a semiconductor integrated circuit device to meet the demand of increase in the integration density and microminiaturization in the semiconductor integrated circuit device. In particular, the photolithographic technique is the basic technology in pattern formation. Photolithography is the technique to transfer the pattern on a mask onto a photoresist applied on a wafer plane by an exposure apparatus.
The basic optical system of an exposure apparatus will be described first. Referring to FIG. 27, exposure light emitted from a light source such as a KrF excimer laser (not shown) passes through a condenser lens 4 by a fly eye lens 2 (light source plane) formed of a group of microlens to be directed to a mask 6.
The exposure light emitted from each microlens is directed all over mask 6 through condenser lens 4. The exposure light particularly passing through the microlens in the proximity of the center of the optical axis is directed substantially perpendicular to the plane of mask 6. In contrast, the exposure light passing through the microlens located at the peripheral area is directed to the plane of mask 6 in an oblique manner. Therefore, an aperture having an opening formed at a predetermined position is arranged in the proximity of fly eye lens 2 so that the exposure light is directed to the plane of mask 6 at an appropriate incident angle.
The exposure light directed to mask 6 is diffracted by the pattern on mask 6. The diffracted light is subjected to Fourier transform by a projection lens 8, whereby a transform image thereof is formed on a pupil plane 10. The transform image is subjected to inverse Fourier transform, whereby an optical image of the pattern is formed on an image plane 12 (wafer plane).
Whether an optical image of the pattern is formed on image plane 12 or not depends upon the incident angle of the exposure light onto the plane of mask 6 and the diffraction angle of the exposure light. The irradiation of mask 6 on which a line and spacer pattern is formed with only perpendicular exposure light will be described with reference to FIGS. 28(a)-28(f).
The diffraction angle .theta. of the exposure light passing through the line and space pattern is represented as: EQU sin .theta.=n.lambda./pitch (n=0, .+-.1, . . . )
Here, the pitch is the sum of the line width and space. .lambda. is the wavelength of the light source.
It is appreciated from the above expression that the diffraction angle becomes greater as the value of the pitch is smaller, and that the diffraction angle becomes smaller as the value of the pitch becomes greater.
When the line and space pattern of masks 6a and 6b is relatively coarse as shown in FIGS. 28(a) and (b), the diffraction angle of the exposure light is relatively small, so that .+-. first order diffracted light 14b and 14c pass through pupil plane 10.
By the interference of zero order diffracted light 14a and .+-. first order diffracted light 14b and 14c, optical images 16a and 16b of the pattern are formed on image plane 12 as shown in FIGS. 23(d) and 23(e).
However, when the line and space pattern of mask 6c is dense as shown in FIG. 28(c), the diffraction angle of the exposure light becomes greater. Therefore, .+-. first order diffracted light 14b and 14c cannot pass through pupil plane 10. Only zero order diffracted light 14a passes through pupil plane 10.
As a result, an optical image of the pattern cannot be formed on image plane 12 as shown in FIG. 28(f). In other words, an optical image of a fine pattern cannot be formed by the method of directing the exposure light perpendicular to the mask.
There is a method of providing some margin in the incident angle of the exposure light towards the mask so that an optical image of a fine pattern can be formed. This method employs an aperture of a greater opening diameter so that the exposure light emitted from the periphery of fly eye lens 2 is directed to the mask.
As shown in FIGS. 29(a)-29(c), exposure light 3a, 3b and 3c is directed to the mask at different angles by an aperture 52. When the line and space pattern of masks 6a and 6b is relatively coarse as shown in FIGS. 29(a) and 29(b), the .+-. first order diffracted light of every exposure light 3a, 3b and 3c pass through pupil plane 10. As a result, optical images 16a and 16b of the pattern can be formed on image plane 12 as shown in FIGS. 29(d) and 29(e).
When the line and space pattern of mask 6c is more dense as shown in FIG. 29(c), a portion of zero order diffracted light 14a and .+-. first order diffracted light 14b of exposure light 3c and a portion of zero order diffracted light 14a and -1 order diffracted light 14c of exposure light 3b pass through pupil plane 10. Although the image quality is not complete, an optical image 16d of the pattern is formed as shown in FIG. 29(f).
For a fine pattern, an optical image of the pattern cannot be formed according to the method in which the exposure light is directed perpendicular to the mask whereas an optical image of the pattern can be formed according to the method in which exposure light directed oblique to the mask is included.
In the above-described method of directing two exposure light to the mask, the zero order diffracted light and .+-. first order diffracted light contribute to formation of an optical image. In other words, an optical image can be formed on the image plane by the interference of the three luminous flux. However, in the fine pattern shown in FIGS. 28(c) and 29(c), .+-. first order diffracted light 14b and 14c of exposure light 3a directed perpendicular to mask 6c cannot pass through pupil plane 10. Only zero order diffracted light 14a passes through pupil plane 10 as shown in FIG. 30(a). The zero order diffracted light is greater in intensity than the first order diffracted light, so that the contrast of the optical image is reduced as shown in FIG. 30(b).
In view of the foregoing, a method is proposed to correspond to microminiaturization, wherein exposure light directed perpendicular to the mask is blocked, and exposure is carried out only by the light directed oblique to the mask.
In this case, an aperture 53 having the center area blocked is employed as shown in FIG. 31(a) to block any exposure light directed perpendicular to mask 6c. This method employing such an aperture 53 is referred to as modified illumination, particularly annular illumination, from the configuration of the aperture. The previously-described two methods are referred to as normal illumination.
In the annular illumination, zero order diffracted light 14a and first order diffracted light 14b of exposure light 3c pass through pupil plane 10. An optical image 16e can be formed on image plane 12 as shown in FIG. 31(b).
This is particularly called double-beam interference since an optical image is formed by the interference of two beams of zero order diffracted light 14a and first order diffracted light 14b.
In double-beam interference, the phase of the exposure light passing through from the opening adjacent to the pattern of mask 6d should be shifted by .pi., as shown in FIG. 32, according to the Huygens principle. The phase difference of the exposure light can be shifted by just .pi. by the method of adjusting the incident angle towards the mask. For example, as shown in FIG. 33, the incident angle to the mask is adjusted so that the light path difference of exposure light 3d arriving at the opening portion of mask 6d is shifted by just the phase of .pi.. In this case, the incident angle of the exposure light must be altered according to the pattern.
There is also the method of using a phase shift mask 6e as shown in FIG. 34. Phase shift mask 6e has a phase shifter 6 provided at every one adjacent opening of mask 6e. A phase difference .pi. is generated between the exposure light passing through phase shifter 6f and the exposure light that does not pass through.
The aperture employed in annular illumination includes a 50% zone aperture, 60% zone aperture, and the like depending upon the ratio of the area blocking the exposure light to the entire area of the aperture. This ratio becomes greater for an aperture corresponding to a finer pattern. However, the aperture employed in annular illumination is not intended to improve the resolution of a particular pattern. It slightly improves the resolution of an undefined pattern.
The feature of the above exposure method by modified illumination will be described in recapitulation in comparison with the exposure method by normal illumination.
In the case of normal illumination with a relatively small pitch as shown in FIG. 35, the diffraction angle of .+-. first order diffracted light 14b and 14c of exposure light 3a directed perpendicular to mask 6c is relatively great. Therefore, .+-. first order diffracted light 14b and 14c cannot pass through pupil plane 10. As a result, an optical image of the pattern cannot be formed on the image plane.
In modified illumination, only - first order diffracted light 14c cannot pass through pupil plane 10 out of the .+-. first order diffracted light 14b and 14c of exposure light 3c directed oblique to mask 6c. + first order diffracted light 14b and zero order diffracted light 14a can pass through pupil plane 10. Therefore, an optical image of the pattern can be formed on the image plane.
In the case of normal illumination with a relatively great pitch, the diffraction angle of the diffracted light of exposure light 3a directed perpendicular to mask 6a is relatively small. Therefore, the diffracted light of a high order including the .+-. first order diffracted light can pass through pupil plane 10. As a result, an optical image of the pattern can be formed on the image plane.
In modified illumination, the diffraction angle of the diffracted light of exposure light 3c directed oblique to mask 6a is relatively small. Therefore, the diffracted light of high order including the + first order diffracted light can pass through pupil plane 10. As a result, an optical image of the pattern can be formed on the image plane.
Particularly when the pitch is great, there is no great difference in the distribution of the diffracted light passing through the pupil plane between normal illumination and modified illumination. Therefore, it can be said that modified illumination is effective for a fine line and space pattern, and not so effective for a relatively great line and space pattern. The level thereof is equal to that of normal illumination.
The exposure method of modified illumination had the problem that the resolution of the line and space pattern is degraded as the pitch is altered even if the line width is constant. There is also the problem that the amount of change in the finish dimension of the line is altered depending upon the modified illumination due to the light proximity effect. This light proximity effect is a phenomenon in which the line (interconnection) finish dimension is altered depending upon the space (distance) from an adjacent line.
The former problem will be described first. In modified illumination, zero order diffracted light and + first order diffracted light of exposure light 3c directed oblique to mask 6c pass through pupil plane 10 as shown in FIG. 36(a). As a result, an optical image 16e is formed at the image plane as shown in FIG. 36(d).
When the space is increased (pitch increased) with a constant line width, the diffraction angle of the exposure light becomes smaller. In this case, the diffracted light of high order including the first order diffracted light passes through pupil plane 10 as shown in FIG. 36(b). The diffracted light passing through pupil plane 10 is directed to image plane 12 through projection lens 8. Here, the incident angle .theta..sub.1 of the diffracted light passing through the neighborhood of pupil plane 10 becomes greater. The relationship of: EQU DOF=k.multidot..lambda./(sin .theta.).sup.2,
where k is a proportional constant is established between the incident angle .theta. of the diffracted light and the value of the depth of focus DOF. Therefore, the depth of focus becomes smaller as the value of .theta. becomes greater.
This depth of focus is the focus range that can maintain a constant image formation performance. Therefore, a smaller value of the depth of focus means that the focus range is narrowed. Therefore, the resolution of the optical image is degraded. As a result, there is a possibility that an optical image is not formed as shown in FIG. 36(e), particularly in the case of a defocus situation.
When the space is further reduced (smaller pitch) with a constant line width, the diffraction angle of the exposure light is further increased. In this case, + first order diffracted light 14b passes through a region more close to pupil plane 10 as shown in FIG. 36(c). The incident angle .theta..sub.2 of + first order diffracted light 14b into image plane 12 becomes greater. Therefore, the depth of focus becomes smaller, similar to the case of FIG. 36(b). As a result, there is a possibility that an optical image is not formed as shown in FIG. 36(f), particularly in the case of a defocus state.
When the line width is altered with the space set constant, the diffraction angle of the diffracted light changes since the pitch is altered. Therefore, a similar phenomenon occurs.
The above description implies that, when modified illumination is employed in patterning the interconnection where the width of the interconnection pattern is set minimum in a semiconductor device, an image of a pattern that has the spacing between interconnections exceed a certain value cannot be formed.
Also, even if the minimum space is set, an image of a pattern in which the width of an interconnection located adjacent to the space exceeds a certain value cannot be formed.
Thus, the interconnection width and the like of an interconnection pattern cannot be easily determined in designing a semiconductor device.
The latter problem will be described hereinafter.
FIG. 37(a) shows the assessment of a simulation in the variance in the finished dimension of the interconnection width when space S is altered with a constant interconnection width L in the interconnection pattern of FIG. 37(b). The interconnection width is set to 0.22 .mu.m. The finish dimension of the interconnection was strongly influenced by the light proximity effect as the space is increased to become smaller than the predetermined dimension for both the 1/2 annular illumination and 2/3 annular illumination. Although the dimension gradually approaches the predetermined dimension as the space is further increased, there was still a difference from the predetermined dimension. It was found that the difference differs between the 1/2 annular illumination and 2/3 annular illumination and depends upon the configuration of the aperture.